Diagonalization Method to Hyperbolic Two-Temperature Generalized Thermoelastic Solid Sphere under Mechanical Damage Effect

This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage. The fundamental equations were derived using the hyperbolic two-temperature generalized thermoelasticity theory with mechanical damage taken into account. The outer surface of the sphere has been assumed to have been shocked thermally without cubical dilatation. The numerical results for the dynamical and conductive temperatures increment, strain, displacement, and average of the principal stresses components have been represented graphically with different values of the hyperbolic two-temperature parameter and mechanical damage parameters. The two-temperature model parameter and the mechanical damage parameter have significant effects. The propagations of the thermomechanical waves take place at finite speeds in the context of the hyperbolic two-temperature theory as well as in the usual context of the Lord–Shulman theory with one-temperature.

Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced model can be formulated by combining the Green–Naghdi Type III and Lord–Shulman models. Eringen’s non-local theory has also been applied to demonstrate the effect of thermoelastic materials which depends on small scale. Some special cases as well as previous thermoelasticity models are deduced from the presented approach. In the domain of the Laplace transform, the system of equations is expressed and the problem is solved using state space method. The converted physical expressions are numerically reversed by Zakian’s computational algorithm. The analysis indicates the significant influence on field variables of non-local modulus and magnetic field with larger values. Moreover, with the established literature, the numerical results are satisfactorily examined.

Thermal-stress analysis of a damaged solid sphere using hyperbolic two-temperature generalized thermoelasticity theory

This work aims to study the influence of the rotation on a thermoelastic solid sphere in the context of the hyperbolic two-temperature generalized thermoelasticity theory based on the mechanical damage consideration. Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed. The governing equations have been written in the context of hyperbolic two-temperature generalized thermoelasticity theory. The bounding surface of the sphere is thermally shocked and without volumetric deformation. The singularities of the studied functions at the center of the sphere have been deleted using L’Hopital’s rule. The numerical results have been represented graphically with various mechanical damage values, two-temperature parameters, and rotation parameter values. The two-temperature parameter has significant effects on all the studied functions. Damage and rotation have a major impact on deformation, displacement, stress, and stress–strain energy, while their effects on conductive and dynamical temperature rise are minimal. The thermal and mechanical waves propagate with finite speeds on the thermoelastic body in the hyperbolic two-temperature theory and the one-temperature theory (Lord-Shulman model).